What if you don't use a cap at all, then overamplify with an op-amp to sky the voltage as soon as you have any rectified signal at all? The op-amp will just max out at its positive input voltage. This assumes you don't need a high power output....

I had no particular time scale or frequency in mind. Well, I was working with a frequency of 100Hz, but thinking of the general case of a digital-like signal, where the "high" sections are a sine wave, and I want to make it more digital-like. "Demodulation" put me on the right track.